greetings

@FenderLesPaul yo

help me with gr

pls

@obe I'm at the library atm so I can help but I can't skype unfortunately

it's ok talk here.

ok

wait a minute

i'm on 3.7, and i don't need help yet.

sorry, uh i will soon though.

$$\frac{D}{d\lambda}\frac{dx^\mu}{d\lambda} = 0$$

how does that become the geodesic equation with the christoffell symbol and stuff.

because that equation is equivalent to $u^{\mu}\nabla_{\mu}u^{\nu} = 0$

oh right

wait what does the $D$ represent in this case?

that's my main confusion.

it's a covariant derivative along the integral curve of $u^{\mu}$

ok.

thanks.

$\frac{D}{d\lambda} \equiv u^{\mu}\nabla_{\mu}$

Note I'm using $u^{\mu}$ simply out of habit

right the letters don't matter.

the equation you wrote need not be from the 4-velocity of a massive particle

it could be a space-like or null geodesic

so a more general 4-vector would probably be better to use

for clarity

@FenderLesPaul Do you think you could possibly offer me 30-50 minutes of GR discussion sometime this week?

I need to clarify a lot of things from before.

Yeah sometime Friday or Saturday would be ideal

Ok, cool.

because I have to finish writing a revised version of a paper we're sending to a journal so until then I'm going to be a bit more busy than usual

modulo wasting a lot of time on this chat

;D

I forgot what university are you attending?

Cornell

Cool. I'm only 500km away.

heh

@FenderLesPaul Take a look at these lecture notes.

Hypothetically would it be possible to learn from them by learning the QM as required as the course progresses?

I need to know if I should finish as much QM as possible or to go through the lectures instead while learning QM I require.

depends on what you mean by "learn"

i.e. how much you expect to get out of it

It's definitely possible to learn them together in parallel, I know one person who has done it, but it's really not a good idea because the amount you'll learn is very little

you won't have a very firm understanding of QFT if you learn QM in parallel

but you can certainly survive the course sure

whether or not that's fine is up to you

@0celo7 What's your opinion?

@FenderLesPaul Hmm...

Do you think you can give me brief list of topics required to study qft from qm?

I think I will only have time to learn the requirement only, and the rest later.

ACM gave me a list a few weeks ago.

you basically need to know everything in Sakurai

harmonic oscillator, spin, angular momentum, perturbation theory.

is that enough?

I still think it would be better to have a firm understanding of QM before beginning QFT instead of just learning what's "necessary".

No time.

@obe yes it's enough if you want to just barely scrape through

assuming you're also going to do the associated problems

Excellent.

you could probably get away with knowing harmonic oscillator, Fermi's golden rule, and knowing how to get irreps of rotation group using raising and lowering operators

but I still concur wholeheartedly with @ACuriousMind

Uncertainty principle is all you need.

@FenderLesPaul only everything in sakurai?

>only

It sounds reasonable.

@obe when do you want the GR discussion

I can maybe do 30 minutes tonight

Yes if you go through Sakurai (I mean like most of it, you don't need to know it cover to cover)

then you'll be truly fine

more than ready

@0celo7 I can't do it today. ;( Is tomorrow or saturday ok for you?

@FenderLesPaul If you would please, look for all the parts of sakuraii i can skip, it would be helpful.

of course not in detail, though an idea.

0celo7 told me what to skip in other books.

@obe maybe tomorrow

@FenderLesPaul do you have any insight into that problem?

@ACuriousMind if you're still awake, I'd appreciate a clue

@obe I agree with the tenor

@0celo7 For that analysis question?

@ACuriousMind ja

wth, since when do we have Chinese spambots here?

wat

Korean

(you can't tell Chinese from Korean!?)

Mh, you're probably right

Korean.

ok, a mystery was solved

We need the "smoke detector."

it turns out the class that uses that book has another prereq that I didn't see: analysis 1

@0celo7 We had established that $\lvert b_n - a \rvert \leq \sum_{i = 1}^n \frac{\lvert a_i - a \rvert}{n}$, right?

ja

Now, for some fixed $\epsilon > 0$, what do we know?

$\exists i :|a_i-a|<\epsilon$

and for all terms that come later, the same thing

Exactly

a hint please

this is really supposed to be a learning thing

Yeah, I'm thinking how to formulate it without solving the exercise

@Rigor If you want, an instance can be made active in this chat.

One would have to poke Undo to get it deployed.

@NormalHuman thanks for the offer

But looks like you don't need it anymore: Korean characters are now blocked.

Great job.

@0celo7 Divide the sum at that $i$.

(It wasn't me, I'm just reporting.) But yes, good job by whoever did that.

:(

I still don't see it

$|b_n-a|\le\sum_{i=1}^{j-1} \frac{|a_i-a|}{n}+\sum_{i=j}^n\frac{\epsilon}{n}$

maybe?

I made $j$ be where the split should occur

Yes, it's correct

I'm sorry if this should be obvious

@ACuriousMind should I sum the epsilons now?

@0celo7 Not necessarily. Does it get us closer to having $< \epsilon$ on the r.h.s.?

@ACuriousMind Well it gets rid of a summation, so yes?

Go on then, these proof are really trial-and-error sometimes

The sum is $(n-j)\epsilon/n$.

I have no clue what to do with the first sum :/

Hint: $n$ is not fixed.

ok so I set $\sum_{i=1}^{j-1}\frac{|a_i-a|}{n}+\frac{(n-j)}{n}\epsilon<\epsilon$ and show that there is an $n$ for which this is true?

Yep

am I done or do I have to solve for $n$ or what?

What do you mean "am I done"? Have you shown the existence of such an $n$? (It's somewhat obvious, but I'd have had to calculate it explicitly in my first analysis course)

uh I can't figure out how to find it explicitly

:/

Yeah, you should give a lower bound for $n$, not an upper one.

I'm bad at quadratics

moment

...quadratics?

dude I can't get it

I always get a less than

@ACuriousMind is this not a quadratic inequality for $n$?

like I get $n^2-(j+1)n+\epsilon^{-1}\sum|a_i-a|<0$

I have no idea how you get the squared $n$ in there

Ah, one moment

multiply through by $n$ to get it out from the denominator

oh

I'm really bad at math

seriously

o.O now the $n$s cancel

@ACuriousMind seriously, all dependence on $n$ drops out D:

This approach seems to not give a proper bound for $n$, it's probably too tight - use $\frac{n-j}{n}\epsilon < \epsilon$ first and then say that for any $\epsilon'$, you choose $\epsilon = \epsilon'/2$. This gives $\sum_{i = 1}^{j-1} \frac{\lvert a_i - a \rvert}{n} < \epsilon'/2$, which has a proper bound.

uh what

That's what I meant with trial-and-error - if one attempt doesn't give a bound, be a bit more lazy in the inequalities.

I have to sleep now

@ACuriousMind be honest: should I be struggling this much?

I recall struggling with my first $\epsilon$-$\delta$ proofs as well, you should get used to this stuff after you've seen it hundreds of times in slight variations :P

It really bothers me that I can do QM and GR exercises and proofs with far less trouble than this

Gamers beware of windows 10.

@0celo7 that's because QM and GR are really easy when it comes to textbook problems

analysis is a whole different beast

it's to be expected

@0celo7 sometimes what physicists mistake for a proof is rather something else, such as intuition...and intuition is important, but easier than a proof ;-P

hey

yo

@Rigor Gamers beware?

I can't believe "piracy advocates" are a thing.

they are

How fucking entitled do you have to be to sit there and think "I have a right to other people's intellectual property"

I believe it's one of those things people do because they can get away with it.

I'm not talking about piracy.

I'm talking about piracy advocacy.

"I want free shit" I can get.

"I deserve free shit" is unbelievable.

True, it shouldn't be a right.

@0celo7 the implicit question is, how well do you trust future-Microsoft to correctly decide what is a pirated game and what isn't? Or what counts as unauthorized hardware and what doesn't? Bear in mind that this article comes from the perspective of people who don't have that trust, or at least don't take it for granted.

Also it's privacy advocates, not piracy advocates.

@DavidZ Seriously?

yes, seriously

@DavidZ Ok, I should have phrased that better.

My bad.

I mean, you have a point, it's just a different point from what is being discussed in the article.

I misread that while eating breakfast. (Poor excuse, but it's what happened.)

Ya, I just agreed to be polite :P

@ChrisWhite OK, I'll pick that up at the library.

@Slereah : when you read Einstein and Rosen's wormhole paper it's nothing like what you thought it was. It's about representing a particle as a "bridge" between two sheets. It isn't about wormholes as they're discussed today.

@JohnDuffield Yes.

Topologically it is identical, though

Somewhat reminescent of the geometrodynamic of Wheeler

@Slereah : some authors appeal to Einstein's authority whilst saying something very different, or even flatly contradicting him. Wheeler didn't understand the difference between curved spacetime and curved space. If he had, he wouldn't have talked about the geon. He would have talked about the electron.

Hm, are we always guaranteed a thermal state in any QFT?

@Slereah What do you mean with "guaranteed"?

you only find "guarantees" in math :P

As in it is always possible to have a thermal state in the Hilbert space of the theory

@Slereah What would forbid you to just write down the density matrix $\mathrm{e}^{-\beta H}$ for it?

True

what got removed

@ACuriousMind what are you hiding from me

my master made a possible typo

He was wondering if there was a sign error

@ACuriousMind does not make sign errors

unless he's talking about gauge covariant derivatives

in which case he does whatever he pleases

$D_\mu=\partial_\mu+\eta\mathrm{i}A_\mu$ where $\eta=\pm 1$ depending on the phase of the moon

Does the sign matter?

Can't you do like

$\partial_\mu + e^{i\alpha} A_\mu$

it probably does not matter

but it's nice for consistency

I seem to recall that $i$ is just some basis element of $U(1)$

@ACuriousMind So after close discussion with my honors mentor (who is a super cool chemical engi/math double major), we figured out that the course that uses that book is actually the second analysis course. The first one has course description: "Introduction to the theory of the real number system. Limits of sequences and functions of a real variable."

That makes me feel a lot better because I can't handle Jost yet.

So next year I'll do Analysis 1 and some other class...have to decide between Topology and Abstract Algebra most likely.

(Or I could do both and go for 20 hours.)

@Slereah Why don't you mathrm?

ACM looks on with disdain

wot

@Slereah No, you can't choose a phase because the whole expression is meant to be real. The $\mathrm{i}$ only ever appears because physicists have a fetish for self-adjoint operators-

What is the engineer's favorite fetish?

Duct tape?

They like to write $i$ as $j$

Ok, ordered Carothers.

@Slereah I swear to Christ if my undergrad thesis has to have $j$...

I'll have to point out that $i\ne\mathrm{i}$ and they need to get glasses.

@ACuriousMind Why are physical constants written in italics?

Is it only pure math constants that are mathrm?

I don't think there's a really consistent logic behind that.

@ACuriousMind Mathematical Physicists are not consistently logical? Tsk.

@0celo7 that's only because they aren't consistently logical

bonjour

ca va?

faints under pressure from not knowing any more French

we've been over this before

last time you said "bien"

I told you it was more appropriate to say "oui"

depending on what dialect of French you use

oui

mon dieu

:(

The education system failed to teach french.

Well French is irrelevant, so

You shouldn't learn another language based off one you already know.

in USA, that's not bad. It's our official language, not yours

@obe why not? that's a great way to get more practice with learning new languages

I wouldn't mind but

I took 4 years of french in HS

and don't remember any of it

how can you take 4 years in HS and not remember any?

that's all I took

plus every year in elementary school

but that stuff doesn't count

People take 4 years of math in high school and a lot don't remember any

And French is arguably less useful than math

do they take 4 years of math? I know you are required to take 2, but everyone I know who took a full 4 remembers how to do algebra and some basic trigonometry

@0celo7 Not going to argue with that

I think it's objectively true

@Jim It's flawed because you have to constantly refer to your own language when trying to use the other one.

Where as if you learn the language by itself, without reference to english, it will be more fluid i guess.

oh, I get it. You and I had a different understanding. I thought you meant "don't learn French if you already know Latin"

or something along those lines

@Jim unfortunately my school didn't care about anything other than math/physics/debate

so language classes were really shitty

we didn't learn anything

music classes were also really shitty

I had to spend a lot of money outside of school to get the kind of music education I desired

amazon.com/Introductory-Analysis-Dover-Books-Mathematics/dp/…

this looks like it starts out nice

@FenderLesPaul unfortunately my school didn't cared about...uh...

hmm, what did they do well...

Uh the AP Stat pass rate was really good?

dope

Although we were miles below the national average for Calc AB.

@ChrisWhite No.

Calc BC has ~50% 5s and e.g. AP World has ~5% 5s.

totalregistration.net/AP-Exam-Registration-Service/…

I wonder how they obtain the scores...I know there is some curving going on.

@MarkMitchison hello?

@ChrisWhite Just like true world-history-ignorant Americans. Sounds about right.

Does anybody know what the status of Hawking's Chronology Projection Conjecture is? Is it accepted as possibly likely, or is it considered dubious?

Someone on Worldbuilding tried to invoke it to make wormholes possible (ignoring some other issues) and I'm trying to shoot it down.

Man it's already Thursday

shivers

@FenderLesPaul Up till now I didn't know what day it was :D

hallo

@ACuriousMind sounds like a mathematician

@FenderLesPaul Why would mathematicians be known for not knowing the day?

@ACuriousMind due to being just slightly more out of touch with reality than everyone else :p

Ah, alright :D

there was a girl in my old topology class that was really out of touch with reality

I thought it was the cutest quirk

:p

@HDE226868 ask @Slereah, he's into recent spacetime topology stuff

@0celo7 Thanks.

@Slereah ^

My spacetime topology is current to 1972 :)

Actually HE is '73...

@FenderLesPaul I think @ACuriousMind is a closet mathematician.

He's reporting on us back to St. Prof. Dr. Groethendiek in Math Nirvana.

The thought that he is Groethendiek has crossed my mind, but I can't imagine Dr. G playing PoE.

It's Grothendieck, not Groethendiek.

@ACuriousMind only the man himself would know that...

My god

@ACuriousMind lol I made my best guess, you're lucky autocorrect didn't make it like great d**k or something

@NeuroFuzzy thanks for suggesting Carolina in my mind

I'm in love with it now

singing it and doing James Taylor's rather unusual fingerpicking is a bit annoying but the song is worth it!

More like Grothendick

@HDE226868 It is pretty likely but as far as I'm aware, they do not have any theorem that covers all possible cases

@Slereah Okay, thanks.

The instability of the quantum vacuum is probably the strongest argument

But I'm not sure it applies generically to all spacetimes

cf my question here : physics.stackexchange.com/questions/200896/…

I kinda want to shoot an email at Visser to ask about that

Also it applies only in the semiclassical regime, but I don't think quantum gravity would rescue it

Although you can make the divergence arbitrarily small near the Cauchy horizon, but it still blows up at that point

So odds are pretty good it would not work out

@ChrisWhite Physicists came up with wormholes before writers :p

Also it is possible that wormholes exist in a more subtle way

Such as Planck scale wormholes

Or Euclidian wormholes in Euclidian gravity

I am also curious to know if there's any theory of quantum gravity without CTCs but with off-shell CTC states

But since most QG theories do the time slicing thing, it's hard to really find any

fyi new dwave benchmarking paper, 1st on 1K qubit array for anyone interested, cited on aaronson blog

@ChrisWhite have mixed feelings on it. think there is some near-scapegoating going on about them. personally regard them as innovative & pioneering into terra incognita. recognize they are highly controversial. they seem to "split opinion".

to try to be fair, science is done in a different way in industry vs academia & some of that shows up as conflict here.

@ChrisWhite lol re "Mars One," seem to recall elon musk may be involved there? yes have heard of their several crashes.